If the measure of m<1 =53 and m<2 =67 then m<4>_?

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.

The frequency table shows the results of a survey asking people how many hours they spend online per week. on a piece of paper, draw a histogram to represent the data. then determine which answer choice matches the histogram you drew. in order here is the.. hours online: 0-3, 4-7, 8-11, 12-15, and 16-19. frequency: 5, 8, 10, 8, 7 answer for the question is in the picture! : )

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false. 1^2 + 4^2 + 7^2 + + (3n - 2)^2 = [n(6n^2-3n-1)/2]